Solusi Umum Persamaan Diferensial Biasa Linear Koefisien Konstan dengan Menggunakan Metode Reduksi Orde

Abstract

Differential equations involve derivatives of unknown functions and are widely used in mathematical modeling of various real-world problems. They can be classified based on linearity, homogeneity, coefficients, number of independent variables, degree, and order, thus requiring appropriate solution methods. One commonly used approach is the reduction of order method, which simplifies equations by reducing their order step by step. However, this method generally requires the solution of the corresponding homogeneous equation as an initial step. This study aims to solve nonhomogeneous linear ordinary differential equations of order with constant coefficients using the reduction of order method without determining the homogeneous solution. This research is a theoretical study based on relevant references concerning solution methods and types of differential equations. The procedure consists of two main stages: determining the fundamental symmetric polynomial variables based on the coefficients and constructing a sequence of solutions through first-order linear differential equations obtained from the reduction process. The results show that this method systematically produces the general solution of linear differential equations of order , making it an effective and efficient alternative approach